# Singular Integral Equations in the Lebesgue Spaces with Variable Exponent

@inproceedings{Kokilashvili2003SingularIE, title={Singular Integral Equations in the Lebesgue Spaces with Variable Exponent}, author={Vakhtang M. Kokilashvili and Stefan Samko}, year={2003} }

For the singular integral operators with piecewise continuous coecients there is proved the criterion of Fredholmness and formula for index in the generalized Lebesgue spaces L p(¢) (i) on a finite closed Lyapunov curve i or a curve of bounded rotation. The obtained criterion shows that Fredholmness in this space and the index depend on values of the function p(t) at the discontinuity points of the coecients of the operator, but do not depend on values of p(t) at points of their continuity.

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